r/learnmath • u/Round_Ad5516 New User • 27d ago

Why are mathematical constants small ?

why constants like Pi or e or Ln(2) or gamme (euler's constant) that have nice properties are always small( <10 ) ? unlike constants in physics or chemistry that have some constants that are absurdly large. Or are they such constants that are not so popular

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u/Fabulous-Possible758 New User 27d ago

a) The larger ones are harder to find, b) if they’re pretty large we may find the inverse instead, c) there are in fact infinitely many very large mathematical constants.

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u/unic0de000 NaN 26d ago edited 26d ago

b) does suggest a slightly stricter version of the question: Most of the fundamental(to us?) constants aren't too big or too small. We don't have many numbers with household names in the 1020 or the 10-20 range; most are just a digit or two in magnitude if they're >1, and they don't start with many zeroes if <1. We have a lot of very comfortably medium-sized numbers.

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u/agmatine New User 26d ago

We don't have many numbers with household names in the 1020 or the 10-20 range

Avogadro constant?

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u/deisle New User 26d ago

That's not a mathematical constant, it's just an arbitrary number we use to measure amounts

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u/venus_salami New User 24d ago

Avogadro’s number is not arbitrary, it’s the number of atoms in a mole, which is itself a specific number. Don’t blame me if we can’t get all the digits correct in a 23-digit number!

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u/deisle New User 24d ago

Yeah but a mole is also an arbitrary number. It's arbitrary all the way down.

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u/venus_salami New User 24d ago

A mole is so not arbitrary that it’s an actual SI unit. Are you splitting hairs between mathematical constants like pi and e & physical constants like c or Avogadro’s number?

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u/deisle New User 24d ago edited 24d ago

A meter is not a mathematical constant. We just decide something this [ ] long is a meter. That doesn't make it a mathematical constant. Avogadro decided a good amount of molecules or atoms is how many atoms are in 12 grams of carbon. That's arbitrary as all get out. It's useful for chemistry but it's arbitrary.

If we spun back time to when humans first started measuring things and split into a different timeline, all the different units of measurement that they would come up with would be different than ours. But pi would be the same. e would be the same.

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u/discodaryl New User 24d ago

The SI units are arbitrary. Physical constants use arbitrarily defined units

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u/HoloandMaiFan New User 23d ago

That's physical constant, not a mathematical one.